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J. Bifurcation Chaos"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p> This paper is dedicated to studying the maximum number of crossing limit cycles of discontinuous planar piecewise-linear differential systems with three regions separated by a nonregular line and formed by linear centers and linear Hamiltonian systems without equilibria. There are two types of crossing limit cycles: one that intersects the nonregular line at three points and the other that intersects the nonregular line at four points, named three-point crossing limit cycles and four-point crossing limit cycles, respectively. We prove that the maximum numbers of three-point and four-point crossing limit cycles are three and one, respectively, and both reach their upper bounds. 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